Black Holes and Extra Dimensions
Jonathan Feng
UC Irvine
UCSD Particle Seminar
28 January 2003
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The Standard Model• Many interesting problems, but one obvious one: where’s
gravity?
Gravity is weak, becomes strong at MD ~ 1018 GeV, far beyond experiment
• Suppose SM confined to D = 4, but gravity propagates in n extra dimensions of size L:
For r L, Fgravity ~ 1/r2
For r L, Fgravity ~ 1/r2+n
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…
gravity
EM
Str
engt
h
rMD-1
Gravity in Extra Dimensions
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Strong Gravity at the Electroweak Scale
• If D > 4, MD < 1018 GeV possible
Suppose MD is 1 TeV, the electroweak unification scale
• The number of extra dims n then fixes L
• n=1 excluded by solar system, but n=2, 3,… are allowed by tests of Newtonian gravity
Arkani-Hamed, Dimopoulos, Dvali (1998)
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Tests of Newtonian GravitySt
reng
th o
f D
evia
tion
R
elat
ive
to N
ewto
nain
Gra
vity
Long, C
han, Price; H
oyle et al.
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Kaluza-Klein States
• Extra dimensions of size L towers of Kaluza-Klein particles with masses ~ L-1
• Large extra dims light states
• KK states may appear at colliders, in astrophysics (supernova cooling, etc.), …
f
f f ’
f ’graviton
_ _
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Black Holes
• BH production requires strong gravity, masses or energies above MD
• In 4D, MD ~ 1018 GeV, BHs confined to astrophysics, form by accretion
• But in extra D with MD ~ 1 TeV, BHs may be produced in elementary particle collisions
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• A Schwarzschild BH (Q = J = 0) has radius
• In classical GR, expect a BH to form when two partons pass within rs of each other:
• Assume this, and that MBH = s1/2.
BHs from Particle Collisions
Banks, Fischler (1999)
Myers, Perry (1986)
^
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• Classic study for 4D, b = 0 collision:
MBH ~ 0.8 s1/2
D’Eath, Payne (1992)
• Heuristic argument for b > 0: J > 0 rs rKerr: ~ 0.64 classical
Anchordoqui, Feng, Goldberg, Shapere (2001)
• Classic study generalized to b > 0:
> 0.64 classical ; MBH > 0.71s1/2 for b = 0, MBH > 0.45s1/2 for b = bmax
Eardley, Giddings (2001)
• And to D > 4:
> 1.05 classical ; MBH > 0.6s1/2 for b = 0, MBH > 0.1s1/2 for b = bmax
Yoshino, Nambu (2002)Ida, Oda, Park (2002)
BH Formation
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For low mass black holes, brane, quantum gravity corrections are important. Require:
• Small statistical fluctuations in number of degrees of freedom
• Little back reaction from radiationPreskill, Schwarz, Shapere, Trivedi (1991)
Both require large entropy S ~ rs2+ n .
• BH lifetime >> MBH-1
For n=6, S(5MD) = 27, S(10MD) = 59
(5MD) = 10MBH -1, (10MD) = 12MBH
–1
Giddings, Thomas (2001)
• Brane effects negligible
Semi-classical analysis only valid for MBH > MBHmin = few MD .
Semi-classical Validity
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Black Holes at CollidersWhat is the production rate?
• LHC: ECOM = 14 TeV
pp BH + X
• Find as many as 1 BH produced per second
• Note, however, extreme sensitivity to MBH
min. Dimopoulos, Landsberg (2001)Rizzo (2001)
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Event Characteristics• For microscopic BHs,
~ 10-27 s, decays are essentially instantaneous
• TH ~ 100 GeV, so multiplicity ~ 10
• j : l : : ,G = 75 : 15 : 2 : 8
Emparan, Horowitz, Myers (2000)
• Signal: spherical events with hard leptons, photons De Roeck (2002)
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Black Holes from Cosmic Rays
• Cosmic rays – the high energy frontier
• Observed events with 1019 eV ECOM ~ 100 TeV
• But meager fluxes! Can we harness this energy?
Kampert, Swordy (2001)
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Cosmic Neutrinos
Feng, Shapere (2001)
Many possible UHE particles – use neutrinos:
Ndominates SM processes, since all partons contribute
pN<< pp. Protons are hopeless
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The Signal
• Vertical atm. depth: 10 mwe
Horizontal atm. depth: 360 mwe
• BH: uniform at all depths
pN X: at top of atmosphere
• Signal: deep inclined showers; atmosphere filters out proton, nucleus background
Feng, Shapere (2001)
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Deep Inclined Showers
Coutu, Bertou, Billior (1999)
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Rates
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• Guaranteed: photoproduction
• Choose most conservative: Protheroe, Johnson
Fluxes
Stecker (1979)Hill, Schramm (1985)
Protheroe, Johnson (1996)
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• Additional sources may exist (for example, to solve the GZK problem)
• Below consider only photoproduction; other sources may increase rates by 2 orders of magnitude
Other Sources
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• Showers may be detected by ground arrays and air fluorescence
Current: AGASA (ground),HiRes (air fluor.)
Future: Auger (both)
Apertureshtt p://w
ww
.auger. org
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Auger Observatory
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Apertures
Capelle, Cronin, Parente, Zas (1998)Diaz, Shellard, Amaral (2001)
Anchordoqui, Feng, Goldberg, Shapere (2001)HiRes Collaboration (1994)
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• Lower bounds on MD from absence of BHs at AGASA and HiRes for MBH
min = MD .
• For n > 3, MD > 1.5 – 2.0 TeV, most stringent bounds to date
Current Bounds: AGASA, HiRes
Anchordoqui, Feng, Goldberg, Shapere (2001)
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For MBHmin ~ 10 MD ,
well into classical regime, bounds are comparable to or exceed all other bounds
MBHmin Dependence
Lower bounds on MD for n=1,...,7 from below
xmin = MBHmin/MD
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Future Prospects: Auger
• Auger begins 2004 — can detect ~100 black holes in 3 years
• Provides first chance to see black holes from extra dimensions
mD (
TeV
)
Number of BHs at Auger for n = 7, MBHmin = MD
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Comparison with LHC
• LHC predictions extremely sensitive to MBH
min
• No Auger BHs, MBHmin
>5 MD no LHC BHs
• Of course, we could see events! ...
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Black Hole Identification
• How will you know if you’ve created one?
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S. Harris
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BHs vs. SM
• BH rates may be 1000 times SM rate. But
– large BH large rate
– large flux large rate
• However, consider Earth-skimming neutrinos:
– large flux large rate
– large BH small rateBertou et al. (2001)
Feng, Fisher, Wilczek, Yu (2001)
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Quasi-horizontal (dashed) and Earth-skimming showers (dotted) in 5 years.
SM explanation (BH=0) excluded at high CL.
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What You Could Do With A Black Hole If You Made One
• Discover extra dimensions
• Test Hawking evaporation, BH properties
• Explore last stages of BH evaporation, quantum gravity, information loss problem
• ……
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Additional Possibilities
• Under-ice: AMANDA/IceCube
• Radio: RICE, ANITA
• Space-based: EUSO/OWL
• These may provide BH branching ratios, angular distributions, etc.
Anchordoqui, Goldberg (2001)Emparan, Masip, Rattazzi (2001)
Uehara (2001)Ringwald, Tu (2001)
Ahn, Cavaglia, Olinto (2002)Kowalski, Ringwald, Tu (2002)
Jain, Kar, Panda, Ralston (2002)Alvarez-Muniz, Feng, Halzen, Han, Hooper (2002)
Anchordoqui, Feng, Goldberg (2002)Iyer Dutta, Reno, Sarcevic (2002)
Anchordoqui, Goldberg, Shapere (2002)McKay, etal. (2002)
...
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Conclusions
• Gravity is either intrinsically weak or is strong but diluted by extra dimensions
• If gravity is strong at ~ 1 TeV, we will find black holes in cosmic rays and colliders
Anchordoqui, Feng, Goldberg, Shapere (2001)
MD (
TeV
)